for \(n\ge 6\)  and \(|\chi _{7}\rangle =(1/2)\bigl (|0\rangle +|6\rangle +|9\rangle -|15\rangle \bigr )\)  for \(n=4\) . An argument analogous to the one
in section 2 shows that \(\Omega (a,n)\)  does not vanish for \(|\chi _{7}\rangle \) . In light of Eq. (REF ), for \(n>2\) , \(|\chi _{7}\rangle \)  is different from the \(|GHZ\rangle \) , \(|W\rangle \) , and Dicke
states under SLOCC. It can be further demonstrated that the state \(|\chi _{7}\rangle \)  is entangled. In particular, for four qubits, it was shown in
[1]} that \(|\chi _{7}\rangle \)  is different from the \(|GHZ\rangle \) , \(|W\rangle \)  and Dicke states under SLOCC. We further note that \(|\chi _{7}\rangle =\)  \(|\chi _{5}\rangle \)  for the case of six qubits.
